# from the theory of proveit.numbers.summation¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import a, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Sum, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c))))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\sum_{k = a}^{c} \alpha_{k}\right) = \left(\left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 12
operand: 7
4Operationoperator: 39
operands: 6
5ExprTuple7
6ExprTuple8, 9
7Lambdaparameter: 31
body: 10
8Operationoperator: 12
operand: 15
9Operationoperator: 12
operand: 16
10Conditionalvalue: 22
condition: 14
11ExprTuple15
12Literal
13ExprTuple16
14Operationoperator: 28
operands: 17
15Lambdaparameter: 31
body: 18
16Lambdaparameter: 31
body: 19
17ExprTuple31, 20
18Conditionalvalue: 22
condition: 21
19Conditionalvalue: 22
condition: 23
20Operationoperator: 34
operands: 24
21Operationoperator: 28
operands: 25
22IndexedVarvariable: 26
index: 31
23Operationoperator: 28
operands: 29
24ExprTuple36, 38
25ExprTuple31, 30
26Variable
27ExprTuple31
28Literal
29ExprTuple31, 32
30Operationoperator: 34
operands: 33
31Variable
32Operationoperator: 34
operands: 35
33ExprTuple36, 41
34Literal
35ExprTuple37, 38
36Variable
37Operationoperator: 39
operands: 40
38Variable
39Literal
40ExprTuple41, 42
41Variable
42Literal